As Sales Manager for Montevideo Productions, Inc., you are planning to review the prices you charge clients for television advertisement development. You currently charge each client an hourly development fee of $2,600. With this pricing structure, the demand, measured by the number of contracts Montevideo signs per month, is 24 contracts. This is down 2 contracts from the figure last year, when your company charged only $2,400.

Question

(a) Construct a linear demand equation giving the number of contracts q as a function of the hourly fee p Montevideo charges for development.
q(p)=

(b) On average, Montevideo bills for 40 hours of production time on each contract. Give a formula for the total revenue obtained by charging $p per hour.
R(p)=

(c) The costs to Montevideo Productions are estimated as follows:
Fixed costs: $130,000 per month
Variable costs: $70,000 per contract
Express Montevideo Productions' monthly cost as a function of the number q of contracts.
C(q)=

Express Montevideo Productions' monthly cost as a function of the hourly production charge p.
C(p)=

(d) Express Montevideo Productions' monthly profit as a function of the hourly development fee p.
P(p)

Find the price it should charge to maximize the profit.
p = $___per hour

How should I solve this problem?
Thank you.

Answer 1

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